A Direct Statistical Formulation to Account for Uncertainty in Mechanical Design: Proof-of-Concept

Abstract

Abstract In recent years there has been an increased need to account for uncertainty in design as industry strives to reduce the amount of physical prototyping in favor of faster and cheaper computer simulations. Traditionally, incorporation of uncertainty in design models has been achieved mainly through either Monte Carlo simulations or Mean Value (MV) approximations. The former, while relatively accurate, can be computationally prohibitive. MV approximations on the other hand, trade accuracy for higher computational speed. The proposed direct statistical formulation is a Corrected Mean Value (CMV) approximation. The CMV exploits the correlation between the parameter coefficients of variation and the fractional error incurred using the MV approach to determine appropriate correction factors. Multiplication of the MV approximation by the correction term significantly reduces the error, without sacrificing computational speed. The approach therefore presents a more accurate approximation of the expected value of a function. This paper presents a numerical proof-of-concept of the CMV formulation. Several examples are presented to illustrate the efficacy of the proposed methodology.